which means that \(\nu _\text{QS}\)  is a quasi-limiting distribution for the process \(X\)  (see e.g. [1]}), and
thus a quasi-stationary distribution (QSD) of \(X\)  (see again  [1]}), i.e. a probability measure
\(\nu \)  such that
\(\mathbb {P}_\nu (X_t\in \cdot \mid t<\tau _\partial )=\nu (\cdot ),\quad \forall t\in \mathbb {Z}_+.\) 
